Abstract
We obtain a description of the m-transitive representations of an arbitrary m-group. Some necessary and sufficient conditions are given for an m-group to admit a faithful m-transitive representation. We establish as a corollary that each subdirectly m-indecomposable group admits a faithful m-transitive representation, and so each variety of m-groups is generated by its m-transitive groups.
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References
Giraudet M. and Lukas F., “Groupes á motié ordonnés,” Fund. Math., 139, No. 2, 75–89 (1991).
Kurosh A. G., The Theory of Groups, Chelsea, New York (1960).
Kopytov V. M. and Medvedev N. Ya., The Theory of Lattice-Ordered Groups, Kluwer Acad. Publ., Dordrecht, Boston, and London (1994).
Glass A. M. W., Partially Ordered Groups, World Sci. Publ. Co., Singapore (1999).
Bayanova N. V. and Nikonova O. V., “Reversional automorphisms of lattice-ordered groups,” Siberian Math. J., 36, No. 4, 656–660 (1995).
Zenkov A. V., “On m-transitive groups,” Math. Notes (to be published).
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Original Russian Text Copyright © 2013 Varaksin S.V. and Zenkov A.V.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 54, No. 2, pp. 298–302, March–April, 2013.
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Varaksin, S.V., Zenkov, A.V. On representations of m-groups. Sib Math J 54, 227–230 (2013). https://doi.org/10.1134/S0037446613020067
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DOI: https://doi.org/10.1134/S0037446613020067